Initial Total Mechanical Energy = Final Total Mechanical Energy
(Ei = Ef)
In this instance:
Ei = Gravitational Potential Energy
Ef = Kinetic Energy
In the absence of friction, ALL of the initial potential energy will be changed into kinetic energy at the bottom of the slide. Thus, the maximum kinetic energy of the child will be 1800 J.
The maximum is 1800 J since energy is not created nor destroyed, it is just transformed. In this example, gravitational potential energy is transformed to kinetic energy.
According to the Pythagorean Theorem for calculating the lengths of a right angle triangle's sides, a^2 + b+2 = c^2, where c is the longest side (and the side opposing the right angle). So in your case it would be 150*150 + 70*70 = 27400. And √ 27400 is your answer.
